On Monday, June 16, 2025 at 6:26:36 AM UTC-6 John Clark wrote:
On Sun, Jun 15, 2025 at 10:32 PM Alan Grayson <[email protected]> wrote: *> I fail to see how the EP implies geodesic motion. If true, the proof must be exceedingly subtle.* *I'll try one more time. If you are in freefall then you experience no gravity, so from your perspective your local spacetime is flat and things move in a path that is the shortest distance between two points, a Euclidean straight line.* *Really? The astronauts in the SS are free-falling in the Earth's gravity field and their path is not a straight line. AG* *But from my perspective standing on the Earth's surface you are being affected by gravity and are moving through spacetime that is curved and non-Euclidean. The Equivalence Principle says both points of view are equally valid, but the only way that could be true is if I see you moving in a path that is the shortest distance between two points in 4D non-Euclidean space, and that is a geodesic.* *> If we assume mass/energy somehow causes a distortion in spacetime gemetry, and we hold a test mass spatially at rest in a gravity field, the question "why does it move"* *If you are holding an object and standing motionless on the Earth's surface then you and the object are still following a path through 4D non-Euclidean spacetime because both of you are still moving through time, but that path is NOT a geodesic because a force is being applied to the bottom of your feet. When you release the object its spacetime path suddenly changes to that of a geodesic while your path remains non-geodesic. And things on different spacetime paths is the definition of "movement".* *>>My problem is I don't know what sort of explanation would satisfy you. * *>A possible answer to my question might be the form of the equations of a geodesic path.* *But that's what General Relativity's field equations do! They told Einstein what the geodesic would be in the curved non-Euclidean 4D spacetime 34 million miles from the sun, and it produced an orbit that was slightly different than the orbit Newton said it should have. * * > I'm not sure, but space and time (here proper time) might be intertwinded in such a way that the spatial coordinates are forced to change because time continues to advance.* *But that's what a spacetime map is, it shows the relationship between space and time. If gravity is not involved then the map is flat and the relationship is simple; but if gravity is involved then that relationship changes and becomes more complicated because the map is curved, and the more gravity there is the more curvature there is. * * John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* 6hr -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/e6f1a17a-7d00-43d9-8720-e7bd9b169ad8n%40googlegroups.com.
